document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=588281>Question 588281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to know the amplitude and period of y=4cos(3.14x)+4\r<BR>\n" );
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document.write( "If a graph can be shown that would be helpful as well </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374451 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Amplitude:\r<BR>\n" );
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document.write( "In general, the amplitude of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Acos%28Bx-C%29%2BD ALIGN=MIDDLE  ALT=\"y+=+Acos%28Bx-C%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29 ALIGN=MIDDLE  ALT=\"abs%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In your case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29=abs%284%29=4 ALIGN=MIDDLE  ALT=\"abs%28A%29=abs%284%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the amplitude of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4cos%283.14x%29%2B4 ALIGN=MIDDLE  ALT=\"y=4cos%283.14x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font color=\"red\">4</font>.\r<BR>\n" );
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document.write( "Going back to the general equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Acos%28Bx-C%29%2BD ALIGN=MIDDLE  ALT=\"y+=+Acos%28Bx-C%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=%282pi%29%2FB ALIGN=MIDDLE  ALT=\"T=%282pi%29%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4cos%283.14x%29%2B4 ALIGN=MIDDLE  ALT=\"y=4cos%283.14x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the value of B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=3.14 ALIGN=MIDDLE  ALT=\"B=3.14\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=%282pi%29%2FB+=+%282pi%29%2F%283.14%29+=+2.00101442903809 ALIGN=MIDDLE  ALT=\"T=%282pi%29%2FB+=+%282pi%29%2F%283.14%29+=+2.00101442903809\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the period is approximately <font color=\"red\">2.00101442903809</font>\r<BR>\n" );
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document.write( "Note: this value is close to 2 because 3.14 is close to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you really meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.14 ALIGN=MIDDLE  ALT=\"3.14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the period would truly be 2.\r<BR>\n" );
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document.write( "A graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4cos%283.14x%29%2B4 ALIGN=MIDDLE  ALT=\"y=4cos%283.14x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is shown below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C4cos%283.14x%29%2B4%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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